The length of a metallic wire is ell_{1} when | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Assuming Hooke's law is valid,the tension $T$ is proportional to the extension $\Delta \ell = \ell - \ell_{0}$,where $\ell_{0}$ is the original le

Vedclass · Accepted Answer

$\frac{T_{2}\ell_{1}-T_{1}\ell_{2}}{T_{2}-T_{1}}$

Vedclass · Answer

(C) Assuming Hooke's law is valid,the tension $T$ is proportional to the extension $\Delta \ell = \ell - \ell_{0}$,where $\ell_{0}$ is the original length.$T = k(\ell - \ell_{0})$For the two given states:$T_{1} = k(\ell_{1} - \ell_{0})$  --- $(1)$$T_{2} = k(\ell_{2} - \ell_{0})$  --- $(2)$Dividing equation $(1)$ by $(2)$:$\frac{T_{1}}{T_{2}} = \frac{\ell_{1} - \ell_{0}}{\ell_{2} - \ell_{0}}$Cross-multiplying:$T_{1}(\ell_{2} - \ell_{0}) = T_{2}(\ell_{1} - \ell_{0})$$T_{1}\ell_{2} - T_{1}\ell_{0} = T_{2}\ell_{1} - T_{2}\ell_{0}$Rearranging to solve for $\ell_{0}$:$T_{2}\ell_{0} - T_{1}\ell_{0} = T_{2}\ell_{1} - T_{1}\ell_{2}$$\ell_{0}(T_{2} - T_{1}) = T_{2}\ell_{1} - T_{1}\ell_{2}$$\ell_{0} = \frac{T_{2}\ell_{1} - T_{1}\ell_{2}}{T_{2} - T_{1}}$

The length of a metallic wire is $\ell_{1}$ when the tension in it is $T_{1}$. It is $\ell_{2}$ when the tension is $T_{2}$. The original length of the wire will be ...... .

Similar Questions

Two wires $A$ and $B$ are stretched by the same load. The radius of wire $A$ is double the radius of wire $B$. The stress on the wire $B$ as compared to the stress on the wire $A$ is

One end of a uniform rod of mass $m_1$ and cross-sectional area $A$ is hung from a ceiling. The other end of the rod is supporting a mass $m_2$. The stress at the midpoint of the rod is:

What is strain? Give its units. Define longitudinal stress.

The breaking stress of a wire depends upon

What is stress? Write its unit and dimensional formula.

Vedclass Test Series

Exam Paper Generator

Online Exam Module